Longitudinal studies in medicine are faced with new analysis challenges due to continually advancing measurement and database technologies. Specifically, innovations in molecular assays, medical imaging, and psychological assessment have generated numerous new putative markers of disease progression. Also, advances in electronic data recording now allow longitudinal investigations to collect high-dimensional outcome data measured at a fine time resolution. The overall goals of this proposal are to develop regression methodology, graphical summaries, and software tools for analyzing modern longitudinal biomedical data. The specific areas of emphasis are: 1. Repeated measures and time-dependent accuracy. Biomarkers are measurements that characterize specific aspects of patient health status. With a clinical event time, T iota, analysis of biomarker data will focus both on the predictive survived distribution given the current value of the marker, P[T iota> T I Y iota(s)] where Y iota(s) represents the measured biomarker at time s (or a function of its history), and on the time-dependent accuracy of the biomarker as defined by characteristics of the marker distribution conditional on event time, P[Y iota(s) > c ] T iota = t]. This aim will develop semi-parametric statistical methods to estimate covariate specific longitudinal predictive values and longitudinal accuracy as characterized by measures of sensitivity and specificity. 2. Longitudinal categorical data and likelihood inference. Longitudinal studies now routinely collect patient health information at a large number of time points. Examples include observational studies of the health effects of air pollution, and pharmacodynamic studies of allergy symptoms. In each of these examples daily categorical outcome data is recorded for several months during which ambient exposure (pollution, pollen) also varies. This aim will develop flexible likelihood-based estimation methods for categorical longitudinal data.